Topological velocity inference from spatial transcriptomic data

Incorporating space and time into models of cell fate transition will be a key step toward characterizing how interactions among neighboring cells, local niche factors and cell migration contribute to tissue development. Here we propose Topological Velocity Inference (TopoVelo), a model for jointly inferring spatial and temporal dynamics of cell fate transition from spatial transcriptomic data. TopoVelo extends the RNA velocity framework to model single-cell gene expression dynamics of an entire tissue with spatially coupled differential equations. TopoVelo estimates cell velocity from developing mouse cerebral cortex, learns interpretable spatial cell state dependencies that correlate with the expression of ligand-receptor genes and reveals spatial signatures of mouse neural tube closure. Finally, we generate Slide-seq data from an in vitro model of human development and use TopoVelo to study the spatial patterns of early differentiation. Our work introduces a new dimension into the study of cell fate transitions and lays a foundation for modeling the collective dynamics of cells comprising an entire tissue.